Sine Rule

Whenever we are discussing a triangle and its properties in general, the notation we’ll assume will correspond to the followed triangle:

A triangle follows these basic properties:

(a) \(A + B + C = \pi \)

(b) Triangle inequality: \(a + b > c,\;b + c > a,\;c + a > b\)

These are many other simple properties of a triangle that most of you might be familiar with. In the following pages, we’ll discuss these and other properties, presenting proofs wherever necessary, and discussing applications of these properties.

Property - 1: Sine Rule

The sides of a triangle are proportional to the sines of the angles opposite to them:

\[\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}\]

We discuss the justification for the case that \(\Delta ABC\) is acute:

The sine rule follows from extending this. Similarly, we can prove the sine rule for an obtuse angled or right angled triangle.